where S is the fractional survival per day. The exponential mortality rate is m = –ln(S).
That’s simple, but Mullin and Brooks went on to consider the common case in which
older stages take longer to complete than younger. This made the equations more
interesting (see their paper, or Aksnes & Ohman 1996), but not conceptually different.
Results for P. newmani (Fig. 8.12) compare quite well to those from the elaborate
horizontal method. The problem which recurs with this technique is that sampling
bias is often not constant with stage; older stages for various reasons are often more
susceptible to capture than younger ones (Fig. 8.13), leading to apparently negative
mortality, which is against our biological belief system.
Fig. 8.12 Results of the Mullin–Brooks vertical mortality-rate estimates for the same
data as were used to generate Fig. 8.11.
(^) Mortality rates from the Wood (1994) technique are solid bars (averaged between stage values in Fig. 8.11); those
from the Mullin–Brooks calculation are open bars. (After Aksnes & Ohman 1996.)
Fig. 8.13 Plot of data from Marshall and Orr (1934): time-series estimates of stage
abundance (C1, C2, etc.) of Calanus finmarchicus in Loch Striven. Abundance
integrated through time increases in older stages much more rapidly than expected
from their somewhat longer stage durations. Apparently they are more susceptible to
capture, which is not attributable to mesh size.